Method for controlling configuration of laser induced breakdown and ablation

ABSTRACT

In one aspect the invention provides a method for laser induced breakdown of a material with a pulsed laser beam where the material is characterized by a relationship of fluence breakdown threshold (Fth) versus laser beam pulse width (T) that exhibits an abrupt, rapid, and distinct change or at least a clearly detectable and distinct change in slope at a predetermined laser pulse width value. The method comprises generating a beam of laser pulses in which each pulse has a pulse width equal to or less than the predetermined laser pulse width value. The beam is focused to a point at or beneath the surface of a material where laser induced breakdown is desired.The beam may be used in combination with a mask in the beam path. The beam or mask may be moved in the x, y, and Z directions to produce desired features. The technique can produce features smaller than the spot size and Rayleigh range due to enhanced damage threshold accuracy in the short pulse regime.

GOVERNMENT RIGHTS

This invention was made with government support provided by the Officeof Naval Research and the National Science Foundation under the terms ofNo. STC PHY 8920108. The government has certain rights in the invention.

Notice: More than one reissue application has been filed for the reissueof U.S. Pat. No. 5,656,186. The reissue applications are applicationnumbers 09/366,685 (the present application), which has divisionalapplications 09/775,069 and 09/775,106.

FIELD OF THE INVENTION

This invention relates generally to methods utilizing lasers formodifying internal and external surfaces of material such as by ablationor changing properties in structure of materials. This invention may beused for a variety of materials.

BACKGROUND OF THE INVENTION

Laser induced breakdown of a material causes chemical and physicalchanges, chemical and physical breakdown, disintegration, ablation, andvaporization. Lasers provide good control for procedures which requireprecision such as inscribing a micro pattern. Pulsed rather thancontinuous beams are more effective for many procedures, includingmedical procedures. A pulsed laser beam comprises bursts or pulses oflight which are of very short duration, for example, on the order of 10nanoseconds in duration or less. Typically, these pulses are separatedby periods of quiescence. The peak power of each pulse is relativelyhigh often on the order of gigawatts and capable of intensity on theorder of 10¹³ w/cm². Although the laser beam is focused onto an areahaving a selected diameter, the effect of the beam extends beyond thefocused area or spot to adversely affect peripheral areas adjacent tothe spot. Sometimes the peripheral area affected is several timesgreater than the spot itself. This presents a problem, particularlywhere tissue is affected in a medical procedure. In the field of lasermachining, current lasers using nanosecond pulses cannot producefeatures with a high degree of precision and control, particularly whennonabsorptive wavelengths are used.

It is a general object to provide a method to localize laser inducedbreakdown. Another object is to provide a method to induce breakdown ina preselected pattern in a material or on a material.

SUMMARY OF THE INVENTION

In one aspect the invention provides a method for laser inducedbreakdown of a material with a pulsed laser beam where the material ischaracterized by a relationship of fluence breakdown threshold (F_(th))versus laser beam pulse width (T) that exhibits an abrupt, rapid, anddistinct change or at least a clearly detectable and distinct change inslope at a predetermined laser pulse width value. The method comprisesgenerating a beam of laser pulses in which each pulse has a pulse widthequal to or less than the predetermined laser pulse width value. Thebeam is focused to a point at or beneath the surface of a material wherelaser induced breakdown is desired.

In one aspect, the invention may be understood by further defining thepredetermined laser pulse width as follows: the relationship betweenfluence breakdown threshold and laser pulse defines a curve having afirst portion spanning a range of relatively long (high) pulse widthwhere fluence breakdown threshold (F_(th)) varies with the square rootof pulse width (T^(1/2)). The curve has a second portion spanning arange of short (low) pulse width relative to the first portion. Theproportionality between fluence breakdown threshold and pulse widthdiffer in the first and second portions of the curve and thepredetermined pulse width is that point along the curve between itsfirst and second portions. In other words, the predetermined pulse widthis the point where the F_(th) versus τ_(p) relationship no longerapplies, and, of course, it does not apply for pulse widths shorter thanthe predetermined pulse width.

The scaling of fluence breakdown threshold (F_(th)) as a function ofpulse width (T) is expressed as F_(th) proportional to the square rootof (T^(1/2)) is demonstrated in the pulse width regime to the nanosecondrange. The invention provides methods for operating in pulse widths tothe picosecond and femtosecond regime where we have found that thebreakdown threshold (Fth) does not vary with the square root of pulsewidth (T^(1/2)).

Pulse width duration from nanosecond down to the femtosecond range isaccomplished by generating a short optical pulse having a predeterminedduration from an optical oscillator. Next the short optical pulse isstretched in time by a factor of between about 500 and 10,000 to producea timed stretched optical pulse to be amplified. Then, the timestretched optical pulse is amplified in a solid state amplifying media.This includes combining the time stretched optical pulse with an opticalpulse generated by a second laser used to pump the solid stateamplifying media. The amplified pulse is then recompressed back to itsoriginal pulse duration.

In one embodiment, a laser oscillator generates a very short pulse onthe order of 10 to 100 femtoseconds at a relatively low energy, on theorder of 0.001 to 10 nanojoules. Then, it is stretched to approximately100 picoseconds to 1 nanosecond and 0.001 to 10 nanojoules. Then, it isamplified to typically on the order of 0.001 to 1.000 millijoules and100 picoseconds to 1 nanosecond and then recompressed. In its finalstate it is 10 to 200 femtoseconds and 0.001 to 1.000 millijoules.Although the system for generating the pulse may vary, it is preferredthat the laser medium be sapphire which includes a titanium impurityresponsible for the lasing action.

In one aspect, the method of the invention provides a laser beam whichdefines a spot that has a lateral gaussian profile characterized in thatfluence at or near the center of the beam spot is greater than thethreshold fluence whereby the laser induced breakdown is ablation of anarea within the spot. The maximum intensity is at the very center of thebeam waist. The beam waist is the point in the beam where wave-frontbecomes a perfect plane; that is, its radius of curvature is infinite.This center is at radius R=0 in the x-y axis and along the Z axis, Z=0.This makes it possible to damage material in a very small volume Z=0,R=0. Thus it is possible to make features smaller than spot size in thex-y focal plane and smaller than the Rayleigh range (depth of focus) inthe Z axis. It is preferred that the pulse width duration be in thefemtosecond range although pulse duration of higher value may be used solong as the value is less than the pulse width defined by an abrupt ordiscernable change in slope of fluence breakdown threshold versus laserbeam pulse width.

In another aspect, a diaphragm, disk, or mask is placed in the path ofthe beam to block at least a portion of the beam to cause the beam toassume a desired geometric configuration. In still further aspects,desired beam configurations are achieved by varying beam spot size orthrough Fourier Transform (FT) pulse shaping to cause a specialfrequency distribution to provide a geometric shape.

It is preferred that the beam have an energy in the range of 10 nJ(nanojoules) to 1 millijoule and that the beam have a fluence in therange of 0.1 J/cm² to 100 J/cm² (joules per centimeter square). It ispreferred that the wavelength be in a range of 200 nm (nanometer) to 1μm (micron).

Advantageously, the invention provides a new method for determining theoptimum pulse width duration regime for a specific material and aprocedure for using such regime to produce a precisely configured cut orvoid in or on a material. For a given material the regime isreproducible by the method of the invention. Advantageously, very highintensity results from the method with a modest amount of energy and thespot size can be very small. Damage to adjoining area is minimized whichis particularly important to human and animal tissue.

These and other object features and advantages of the invention will bebecome apparent from the following description of the preferredembodiments, claims, and accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic representation of a laser induced breakdownexperimental system which includes a chirped pulse amplification lasersystem and means for detecting scattered and transmitted energy. If thesample is transparent, then transmitted energy can also be measured.

FIG. 2 is a plot of scattered energy versus incident fluence obtainedfor an opaque (gold) sample using the system in FIG. 1 operated for 150femtoseconds (fs) pulse duration.

FIG. 3 is a plot of calculated and experimental values of thresholdfluence versus pulse width for gold, with experimental values obtainedfor the gold sample using the system of FIG. 1 operated at 800 nmwavelength. The arrow shows the point on the plot where the F_(th)proportional to T^(1/2) no longer applies, as this relationship onlyholds for pulse widths down to a certain level as shown by the solidline.

FIG. 4 is a graphical representation of sub-spot size ablation/machiningin gold based on arbitrary units and showing F_(th) the thresholdfluence needed to initiate material removal; Rs the spot size of theincident beam and Ra the radius of the ablated hole in the x-y plane.

FIG. 5 is a schematic illustration of a beam intensity profile showingthat for laser micro-machining with ultrafast pulse according to theinvention, only the peak of the beam intensity profile exceeds thethreshold intensity for ablation/machining.

FIG. 6A and B are schematic illustrations of a beam showing theplacement of a disk-shaped mask in the beam path.

FIG. 7 is a plot of scattered plasma emission and transmitted laserpulse as a function of incident laser pulse energy for a transparentglass sample, SiO₂.

FIG. 8 is a plot of fluence threshold (F_(th)) versus pulse width (T)for the transparent glass sample of FIG. 7 showing that F_(th) varyingwith T^(1/2) only holds for pulse widths down to a certain level asshown by the solid line. Previous work of others is shown in the longpulse width regime (Squares, Smith Optical Eng 17, 1978 and Triangles.Stokowski, NBS Spec Bul 541, 1978).

FIG. 9 is a plot of fluence threshold versus pulse width for cornealtissue, again showing that the proportionality between F_(th) and pulsewidth follows the T^(1/2) relationship only for pulse widths which arerelatively long.

FIGS. 10 and 11 are plots of plasma emission versus laser fluenceshowing that at 170 (FIG. 10) pulse width the F_(th) is very clearlydefined compared to 7 nm (FIG. 11) pulse width where it is very unclear.

FIG. 12 is a plot of impact ionization rate per unit distance determinedby experiment and theoretical calculation.

FIGS. 13A and B are schematic illustrations of beam profile along thelongitudinal Z axis and sharing precise control of damage—dimensionalong the Z axis.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

Referring to FIG. 1 there is shown an apparatus for performing tests todetermine the laser induced breakdown threshold as a function of laserpulse width in the nanosecond to femtosecond range using a chirped-pulseamplification (CPA) laser system. The basic configuration of such a CPAsystem is described in U.S. Pat. No. 5,235,606 which is assigned to theassignee of the present invention and which has inventors in common withthis present application. U.S. Pat. No. 5,235,606 is incorporated hereinby reference in its entirety.

Chirped-pulse amplification systems have been described by JeffreySquier and Gerard Mourou, two of the joint inventors in the presentapplication, in a publication entitled Laser Focus World published byPennwell in June of 1992. It is described that CPA systems can beroughly divided into four categories. The first includes the high energylow repetition systems such as ND glass lasers with outputs of severaljoules but they may fire less than 1 shot per minute. A second categoryare lasers that have an output of approximately 1 joule and repetitionrates from 1 to 20 hertz. The third group consists of millijoule levellasers that operate at rates ranging from 1 to 10 kilohertz. A fourthgroup of lasers operates at 250 to 350 kilohertz and produces a 1 to 2microjoules per pulse. In U.S. Pat. No. 5,235,606 several solid stateamplifying materials are identified and the invention of U.S. Pat. No.5,235,606 is illustrated using the Alexandrite. The examples below useTi:Sapphire and generally follow the basic process of U.S. Pat. No.5,235,606 with some variations as described below.

The illustrative examples described below generally pertain to pulseenergies less than a microjoule and often in the nanojoule range withpulse duration in the range of hundreds of picoseconds or less and thefrequency on the order of 1 kilohertz. But these examples are merelyillustrative and the invention is not limited thereby.

In a basic scheme for CPA, first a short pulse is generated. Ideally thepulse from the oscillator is sufficiently short so that further pulsecompression is not necessary. After the pulse is produced it isstretched by a grating pair arranged to provide positive group velocitydispersion. The amount the pulse is stretched depends on the amount ofamplification. Below a millijoule, tens of picoseconds are usuallysufficient. A first stage of amplification typically takes place ineither a regenerative or a multipass amplifier. In one configurationthis consists of an optical resonator that contains the gain media, aPockels cell, and a thin film polarizer. After the regenerativeamplification stage the pulse can either be recompressed or furtheramplified. The compressor consists of a grating or grating pair arrangedto provide negative group velocity dispersion. Gratings are used in thecompressor to correspond to those in the stretching stage. Moreparticulars of a typical system are described in U.S. Pat. No.5,235,606, previously incorporated herein by reference.

An important aspect of the invention is the development of acharacteristic curve of fluence breakdown threshold F_(th) as a functionof laser pulse width specific to a material. Then identify on suchcurve, the point at which there is an abrupt, or distinct and rapidchange or at least a discernable change in slope characteristic of thematerial. In general it is more desirable to operate past this pointbecause of the more precise control of the laser induced breakdown (LIB)or ablation threshold.

EXAMPLE 1 Opaque Material

FIG. 1 shows an experimental setup for determining threshold fluence bydetermining scattered energy versus incident fluence and by determiningthreshold fluence versus pulse width. The system includes means forgenerating a pulsed laser beam as described earlier, and means,typically a lens, for collecting emission from the target to aphotomultiplier tube. Change of transmission through a transparentsample is measured with an energy meter.

FIG. 2 shows a plot of data obtained from an absorbing medium which isgold using 150 fs pulse and FIG. 3 shows threshold fluence versus pulsewidth. The arrow in FIG. 3 identifies the point at which therelationship between the threshold fluence and pulse width variesdramatically.

In experimental conditions with wavelength of 800 nm and 200 fs pulseson gold (FIG. 3), the absorption depth is 275 A with a diffusion lengthof 50 A. In the case of nanosecond pulses the diffusion length, which ison the order of 10 μm (micron) in diameter, is much longer than theabsorption depth, resulting in thermal diffusion being the limitingfactor in feature size resolution. Empirical evidence for the existenceof these two regimes is as exhibited in FIG. 3. Here both experimentaland theoretical ablation thresholds are plotted as a function of pulsewidth. An arrow at approximately 7 picoseconds pulse width (designatedherein as T or τ_(p)) delineates the point (or region closely boundingthat point) at which the thermal diffusion length (L_(th)) is equal tothe absorption depth (1/a). It is clear that for a smaller size spot ashorter (smaller) pulse is necessary. For spot size on the order of 1000Å or less, pulse width on the order of 100 femtoseconds or less will beneeded. It is clear from the figure that this is the point at which theablation threshold transitions from a slowly varying or nearly constantvalue as a function of pulse width to one that is dramatically dependenton pulse time. This result is surprising. It has been demonstrated thatthe electron thermalization time for laser deposited energy in gold ison the order of, or less than, 500 fs and the electron-latticeinteraction time is 1 ps. The consequences of this four ultrafast laserpulses is that the energy is contained within the beam spot. In fact forenergies at or near the threshold for ablation, the spatial profile ofthe laser beam will determine the size and shape of the region beingablated (FIGS. 4 and 5).

Additional experiments were performed to measure the amount ofrecombination light produced as a function of the fluence impinging on agold film. The technique involved is based upon the experimental setuppreviously described. A basic assumption is that the intensity of thelight is proportional to the amount of material ablated. In FIG. 4, thematerial removed is plotted as a function of fluence. A well definedthreshold fluence is observed at which material removal is initiated. Byhaving only a small fraction of the gaussian beam where the fluence isgreater than the threshold, the ablated region can be restricted to thissmall area. In FIG. 4, R_(a) is the radial position on the beam wherethe fluence is at threshold. Ablation, then, occurs only within a radiusR_(a). It is evident that by properly choosing the incident fluence, theablated spot or hole can in principle be smaller than the spot size,R_(s). This concept is shown schematically in FIG. 5. Although the datafor a 150 fs pulse is shown in FIG. 4, this threshold behavior isexhibited in a wide range of pulse widths. However, sub spot sizeablation is not possible in the longer pulse regimes, due to thedominance of thermal diffusion as will be described below.

Additional experiments on opaque materials used a 800 nm Ti:Sapphireoscillator whose pulses were stretched by a grating pair, amplified in aregenerative amplifier operating at 1 kHz, and finally recompressed byanother grating pair. Pulse widths from 7 ns to 100 fs were obtained.The beam was focused with a 10× objective, implying a theoretical spotsize of 3.0 μm in diameter. A SEM photo-micrograph of ablated holesobtained in a silver film on glass, using a pulse width of 200 fs and apulse energy of 30 nJ (fluence of 0.4 J/cm²) produced two holes ofdiameter approximately 0.3 μm in diameter. Similar results have beenobtained in aluminum.

These results suggest that by, producing a smaller spot size which is afunction of numerical aperture and wavelength, even smaller holes can bemachined. We have demonstrated the ability to generate the fourthharmonic (200 nm) using a nonlinear crystal. Thus by using a strongerobjective lens along with the 200 nm light, holes with diameters of 200angstroms could in principle be formed.

These examples show that by using femtosecond pulses the spatialresolution of the ablation/machining process can be considerably lessthan the wavelength of the laser radiation used to produce it. Theablated holes have an area or diameter less than the area or diameter ofthe spot size. In the special case of diffraction limited spot size, theablated hole has a size (diameter) less than the fundamental wavelengthsize. We have produced laser ablated holes with diameters less than thespot diameter and with diameters 10% or less of the laser beam spotsize. For ultrafast pulses in metals the thermal diffusion length,l_(th)=(Dt)^(1/2) (where D is the thermal diffusivity and t the pulsetime), is significantly smaller than the absorption depth (1/a), where ais the absorption coefficient for the radiation.

Those skilled in the art will understand that the basic method of theinvention may be utilized in alternative embodiments depending on thedesired configurations of the induced breakdown. Examples include, butare not limited to using a mask in the beam path, varying spot size,adjusting focus position by moving the lens, adjusting laser cavitydesign, Fourier Transform (FT) shaping, using a laser operating modeother than TEMoo, and adjusting the Rayleigh range, the depth of focusor beam waist.

The use of a mask is illustrated in FIG. 6A and B. The basic methodconsists of placing a mask in the beam path or on the target itself. Ifit is desired to block a portion of the beam, the mask should be made ofan opaque material and be suspended in the beam path (FIG. 6)alternatively, the mask may be placed on the target and be absorptive soas to contour the target to the shape of the mask (FIG. 6B).

The varying spot size is accomplished by varying the laster f/#, varyingthe focal length of the lens or input beam size to the lens as byadjustable diaphragm.

Operation in other than the TEMoo mode means that higher ordertransverse modes could be used. This affects the beam and material asfollows: the beam need not be circular or gaussian in intensity. Thematerial will be ablated corresponding to the beam shape.

The Rayleigh range (Z axis) may be adjusted by varying the beamdiameter, where the focal plane is in the x-y axis.

EXAMPLE 2 Transparent Material

A series of tests were performed on an SiO₂ (glass) sample to determinethe laser induced breakdown (LIB) threshold as a function of laser pulsewidth between 150 fs-7 ns, using a CPA laser system. The short pulselaser used was a 10 Hz Ti:Sapphire oscillator amplifier system based onthe CPA technique. The laser pulse was focused by an f=25 cm lens insidethe SiO₂ sample. The Rayleigh length of the focused beam is ˜2 mm. Thefocused spot size was measured in-situ by a microscope objective lens.The measured spot size FWHM (full width at half max) was 26 μm indiameter in a gaussian mode. The fused silica samples were made fromCorning 7940, with a thickness of 0.15 mm. They were optically polishedon both sides with a scratch/dig of 20-10. Each sample was cleaned bymethanol before the experiment. Thin samples were used in order to avoidthe complications of self-focusing of the laser pulses in the bulk. TheSiO₂ sample was mounted on a computer controlled motorized X-Ytranslation stage. Each location on the sample was illuminated by thelaser only once.

Two diagnostics were used to determine the breakdown threshold F_(th).First, the plasma emission from the focal region was collected by a lensto a photomultiplier tube with appropriate filters. Second, the changeof transmission through the sample was measured with an energy meter.(See FIG. 1) Visual inspection was performed to confirm the breakdown ata nanosecond pulse duration. FIG. 7 shows typical plasma emission andtransmitted light signal versus incident laser energy plots, at a laserpulse width of τ_(p)=300 fs. It is worth noting that the transmissionchanged slowly at around F_(th). This can be explained by the temporaland spatial behavior of the breakdown with ultrashort pulses. Due to thespatial variation of the intensity, the breakdown will reach thresholdat the center of the focus, and because of the short pulse duration, thegenerated plasma will stay localized. The decrease in transmitted lightis due to the reflection, scattering, and absorption by the plasma. Byassuming a gaussian profile in both time and space for the laserintensity, and further assuming that the avalanche takes the entirepulse duration to reach threshold, one can show that the transmittedlaser energy U_(t) as a function of the input energy U is given by

U_(t)=kU, U≦U_(th)

U_(t)=kU_(th)[1+ln(U/U_(th))], U>U_(th)

where k is the linear transmission coefficient. The solid curve in FIG.7 is plotted using Eq. (1) with U_(th) as a fitting parameter. Incontrast, breakdown caused by nanosecond laser pulses cuts off thetransmitted beam near the peak of the pulses, indicating a differenttemporal and spatial behavior.

FIG. 8 shows the fluence breakdown threshold F_(th) as a function oflaser pulse width. From 7 ns to about 10 ps, the breakdown thresholdfollows the scaling in the relatively long pulse width regime (trianglesand squares) are also shown as a comparison—it can be seen that thepresent data is consistent with earlier work only in the higher pulsewidth portion of the curve. When the pulse width becomes shorter than afew picoseconds, the threshold starts to increase. As noted earlier withrespect to opaque material (metal), this increased precision at shorterpulse widths is surprising. A large increase in damage thresholdaccuracy is observed, consistent with the multiphoton avalanchebreakdown theory. (See FIGS. 8 and 9). It is possible to make featuressmaller than spot size in the x-y focal plane and smaller than theRayleigh range (depth of focus) in the longitudinal direction or Z axis.These elements are essential to making features smaller than spot sizeor Rayleigh range.

EXAMPLE 3 Tissue

A series of experiments was performed to determine the breakdownthreshold of cornea as a function of laser pulse width between 150 fs-7ns, using a CPA laser system. As noted earlier, in this CPA lasersystem, laser pulse width can be varied while all other experimentalparameters (spot size, wavelength, energy, etc.) remain unchanged. Thelaser was focused to a spot size (FWHM) of 26 μm in diameter. The plasmaemission was recorded as a function of pulse energy in order todetermine the tissue damage threshold. Histologic damage was alsoassessed.

Breakdown thresholds calculated from plasma emission data revealeddeviations from the scaling law. F_(th) α T^(1/2), as in the case ofmetals and glass. As shown in FIG. 9, the scaling law of the fluencethreshold is true to about 10 ps, and fail when the pulse shortens toless than a few picoseconds. As shown in FIGS. 10 and 11, the ablationor LIB threshold varies dramatically at high (long) pulse width. It isvery precise at short pulse width. These results were obtained at 770 nmwavelength. The standard deviation of breakdown threshold measurementsdecreased markedly with shorter pulses. Analysis also revealed lessadjacent histological damage with pulses less than 10 ps.

The breakdown threshold for ultrashort pulses (<10 ps) is less thanlonger pulses and has smaller standard deviations. Reduced adjacenthistological damage to tissue results from the ultrashort laser pulses.

In summary, it has been demonstrated that sub-wavelength holes can bemachined into metal surfaces using femtosecond laser pulses. The effectis physically understood in terms of the thermal diffusion length, overthe time period of the pulse deposition, being less than the absorptiondepth of the incident radiation. The interpretation is further based onthe hole diameter being determined by the lateral gaussian distributionof the pulse in relation to the threshold for vaporization and ablation.

Laser induced optical breakdown dielectrics consists of three generalsteps: free electron generation and multiplication, plasma heating andmaterial deformation or breakdown. Avalanche ionization and multiphotonionization are the two processes responsible for the breakdown. Thelaser induced breakdown threshold in dielectric material depends on thepulse width of the laser pulses. An empirical scaling law of the fluencebreakdown threshold as a function of the pulse width is given by F_(th)α τ_(p), or alternatively, the intensity breakdown threshold,I_(th)=F_(th)/τ_(p). Although this scaling law applies in the pulsewidth regime from nanosecond to tens of picoseconds, the invention takesadvantage of the heretofore unknown regime where breakdown thresholddoes not follow the scaling law when suitably short laser pulses areused, such as shorter than 7 picoseconds for gold and 10 picoseconds forSiO₂.

While not wishing to be held to any particular theory, it is thoughtthat the ionization process of a solid dielectric illuminated by anintense laser pulse can be described by the general equation

dne(t)/dt=η(E)ne(t)+(dne(t)/dt)_(Pl)—(dn_(e)(t)/dt)_(loss)

where n_(e)(t) is the free electron (plasma) density, η(E) is theavalanche coefficient, and E is the electric field strength. The secondterm on the right hand side is the photoionization contribution, and thethird term is the loss due to electron diffusion, recombination, etc.When the pulse width is in the picosecond regime, the loss of theelectron is negligible during the duration of the short pulse.

Photoionization contribution can be estimated by the tunneling rate. Forshort pulses, E˜10⁸ V/cm, the tunneling rate is estimated to be w˜4×10⁹sec⁻¹, which is small compared to that of avalanche, which is derivedbelow. However, photoionization can provide the initial electrons neededfor the avalanche processes at short pulse widths. For example, the datashows at 1 ps, the rms field threshold is about 5×10⁷ V/cm. The fieldwill reach a value of 3.5×10⁷ V/cm (ms) at 0.5 ps before the peak of thepulse, and w˜100 sec⁻¹. During a Δt˜100 fs period the electron densitycan reach n_(e)˜n_(t)[1−exp(−wΔt)]˜10¹¹ cm⁻³, where n_(t)˜10²² is thetotal initial valence band electron density.

Neglecting the last two terms there is the case of an electron avalancheprocess, with impact ionization by primary electrons driven by the laserfield. The electron density is then given by n_(e)(t)=n_(o)×exp(n(E)t),where n_(o) is the initial free electron density. These initialelectrons may be generated through thermal ionization of shallow trapsor photoionization. When assisted by photoionization at short pulseregime, the breakdown is more statistical. According to the conditionthat breakdown occurs when the electron density exceeds n_(th)≅10¹⁸ cm⁻³and an initial density of n_(o)≅19¹⁰ cm⁻³, the breakdown condition isthen given by ητ_(p)≅18. For the experiment, it is more appropriate touse n_(th)≅1.6×10²¹ cm⁻³, the plasma critical density, hence thethreshold is reached when ητ_(p)≅30. There is some arbitrariness in thedefinition of plasma density relating to the breakdown threshold.However, the particular choice of plasma density does not change thedependence of threshold as function of pulse duration (the scaling law).

In the experiment, the applied electric field is on the order of a fewtens of MV/cm and higher. Under such a high field, the electrons have anaverage energy of ˜5 eV, and the electron collision time is less than0.4 fs for electrons with energy U≧5-6 eV. Electrons will make more thanone collision during one period of the electric oscillation. Hence theelectric field is essentially a dc field to those high energy electrons.The breakdown field at optical frequencies has been shown to correspondto dc breakdown field by the relationship E^(rmk) _(th)(w)=E^(dc)_(TH)(1+w²τ²)^(1/2), where w is the optical frequency and τ is thecollision time.

In dc breakdown, the ionization rate per unit length, α, is used todescribe the avalanche process, with η=α(E)v_(drift), where v_(drift) isthe drift velocity of electrons. When the electric field is as high as afew MV/cm, the drift velocity of free electrons is saturated andindependent of the laser electric field, v_(drift)≅2×10⁷ cm/s.

The ionization rate per unit length of an electron is just eE/U_(i)times the probability, P(E), that the electron has an energy ≧U_(i), orα(E)=(eE/U_(i))P(E). Denoting E_(kT,E)p, and E_(i) as threshold fieldsfor electrons to overcome the decelerating effects of thermal, phonon,and ionization scattering, respectively. Then the electric field isnegligible, E<E_(kT), so the distribution is essentially thermal, P(E)is simply exp(−U_(i)/kT). It has been suggested: P(E)˜exp(−const/E) forE_(kT)<E<E_(p); P(E)˜exp(−const/E²) at higher fields (E>E_(p)).Combining the three cases the expression that satisfies both low andhigh field limits:

α(E)=(eE/U_(i))exp(−Ei/(E(1+E/E_(p))+E_(kT)).

This leads to F_(th) α E²τ_(p)˜1/τ_(p), i.e., the fluence threshold willincrease for ultrashort laser pulses when E>E_(p)E_(i) is satisfied.

FIG. 12 is a plot of α as a function of the electric field, E. Fromexperimental data, calculated according to ητ_(p)=30 and η=av_(drift).The solid curve is calculated from the above equation, using E_(i)=30MV/cm, E_(p)=3.2 MV/cm, and E_(kT)=0.01 MV/cm. These parameters arecalculated from U=eEl, where U is the appropriate thermal, phonon, andionization energy, and l is the correspondent energy, relation length(l_(kT)=l_(p)˜5 Å, the atomic spacing, and l_(i)≅30 Å). It shows thesame saturation as the experimented data. The dashed line is correctedby a factor of 1.7, which results in an excellent fit with theexperimental data. This factor of 1.7 is of relatively minor importance,as it can be due to a systematic correction, or because breakdownoccurred on the surface first, which could have a lower threshold. Theuncertainty of the saturation value of v_(drift) also can be a factor.The most important aspect is that the shape (slope) of the curve givenby the equation provides excellent agreement with the experimental data.Thus, the mechanism of laser induced breakdown in fused silica (Example2), using pulses as short as 150 fs and wavelength at 780 nm, is likelystill dominated by the avalanche process.

Opaque and transparent materials have common characteristics in thecurves of FIGS. 3, 8, and 9 each begins with F_(th) versus T^(1/2)behavior but then distinct change from that behavior is evident. Fromthe point of deviation, each curve is not necessarily the same since thematerials differ. The physical characteristics of each material differrequiring a material specific analysis. In the case of SiO₂ (FIG. 8) theenergy deposition mechanism is by dielectric breakdown. The opticalradiation is releasing electrons by multiphoton ionization (M PI) thatare tightly bound and then accelerating them to higher energies by highfield of the laser. It is thought that only a small amount of relativelyhigh energy electrons exist prior to the laser action. The electrons inturn collide with other bound electrons and release them in theavalanching process. In the case of metal, free electrons are availableand instantly absorbing and redistributing energy. For any material, asthe pulses get shorter laser induced breakdown (LIB) or ablation occursonly in the area where the laser intensity exceeds LIB or ablationthreshold. There is essentially insufficient time for the surroundingarea to react thermally. As pulses get shorter, vapor from the ablatedmaterial comes off after the deposition of the pulse, rather than duringdeposition, because the pulse duration is so short. In summary, by themethod of the invention, laser induced breakdown of a material causesthermal-physical changes through ionization, free electronmultiplication, dielectric breakdown, plasma formation, otherthermal-physical changes in state, such as melting and vaporization,leading to an irreversible change in the material. It was also observedthat the laser intensity also varies along the propagation axis (FIG.13). The beam intensity as a function of R and Z expressed as:

l((Z, R)=l_(o)/(1+Z/Z_(R))²−exp(−2R²/W² _(z))

where Z_(R) is the Rayleigh range and is equal to$Z_{R} = \frac{{\pi W}_{o}^{2}}{\lambda}$

W_(o) is the beam size at the waist (Z=0).

We can see that the highest value of the field is at Z=R=0 at the centerof the waist. If the threshold is precisely defined it is possible todamage the material precisely at the waist and have a damaged volumerepresenting only a fraction of the waist in the R direction or in the Zdirection. It is very important to control precisely the damagethreshold or the laser intensity fluctuation.

For example, if the damage threshold or the laser fluctuations knownwithin 10% that means that on the axis (R=0)

I(O,Z)/I_(o)=1(1=(Z/Z_(R))²=0.9

damaged volume can be produced at a distance Z_(R)/3 where Z_(R) againis the Rayleigh range. For a beam waist of W_(o)=λ then$Z_{R} = {\frac{{\pi W}_{o}^{2}}{\lambda} = {\pi\lambda}}$

and the d distance between hole can $Z_{R} = \frac{\pi\lambda}{3}$

as shown in FIG. 13.

The maximum intensity is exactly at the center of the beam waist (Z=0,R=0). For a sharp threshold it is possible to damage transparent,dielectric material in a small volume centered around the origin point(Z=0, R=0). The damage would be much smaller than the beam waist in theR direction. Small cavities, holes, or damage can have dimensionssmaller than the Rayleigh range (Z_(R)) in the volume of thetransparent, dielectric material. In another variation, the lens can bemoved to increase the size of the hole or cavity in the Z direction. Inthis case, the focal point is essentially moved along the Z axis toincrease the longitudinal dimension of the hole or cavity. Thesefeatures are important to the applications described above and torelated applications such as micro machining, integrated circuitmanufacture, and encoding data in data storage media.

Advantageously, the invention identifies the regime where breakdownthreshold fluence does not follow the scaling law and makes use of suchregime to provide greater precision of laser induced breakdown, and toinduce breakdown in a preselected pattern in a material or on amaterial. The invention makes it possible to operate the laser where thebreakdown or ablation threshold becomes essentially accurate. Theaccuracy can be clearly seen by the I-bars along the curves of FIGS. 8and 9. The I-bars consistently show lesser deviation and correspondinglygreater accuracy in the regime at or below the predetermined pulsewidth.

While this invention has been described in terms of certain embodimentthereof, it is not intended that it be limited to the above description,but rather only to the extent set forth in the following claims.

The embodiments of the invention in which an exclusive property orprivilege is claimed are defined in the appended claims.

We claim:
 1. A method for laser induced breakdown (LIB) of a non-biologic material with a pulsed laser beam, the material being characterized by a relationship of fluence breakdown threshold at which breakdown occurs versus laser pulse width that exhibits a rapid and distinct change in slope at a characteristic laser pulse width, said method comprising the steps of: a. generating a beam of at least one or more laser pulses in which each pulse has a pulse width equal to or less than said characteristic laser pulse width; and b. focusing said beam directing said pulse to a point at or beneath the surface of the material.
 2. The method according to claim 1 wherein the material is a metal, the pulse width is 10 to 10,000 femtoseconds, and the beam pulse has an energy of 1 nanojoule to 1 microjoule.
 3. The method according to claim 1 wherein the spot size is varied within a range of 1 to 100 microns by changing the f number of the laser beam.
 4. The method according to claim 1 wherein the spot size is varied within a range of 1 to 100 microns by varying the target position.
 5. The method according to claim 1 wherein the material is transparent to radiation emitted by the laser and the pulse width is 10 to 10,000 femtoseconds, the beam pulse has an energy of 10 nanojoules to 1 millijoule.
 6. The method according to claim 1 wherein the material is biological tissue, the pulse width is 10 to 10,000 femtoseconds and the beam has an energy of 10 nanojoules to 1 millijoule.
 7. A method for laser induced breakdown (LIB) of a material with a pulsed laser beam, the material being characterized by a relationship of fluence breakdown threshold versus laser pulse width that exhibits a rapid and distinct change in slope at a predetermined laser pulse width where the onset of plasma induced breakdown occurs, said method comprising the steps of: a. generating a beam of one or more laser pulses in which each pulse has a pulse width equal to or less than said predetermined laser pulse width obtained by determining the ablation (LIB) threshold of the material as a function of pulse width and by determining where the ablation (LIB) threshold function is no longer proportional to the square root of pulse width; and b. focusing said beam to a point at or beneath the surface of the material.
 8. The method according to claim 1 wherein the laser beam pulse has an energy in a range of 10 nanojoules to 1 millijoule.
 9. The method according to claim 1 wherein the laser beam pulse has a fluence in a range of 100 millijoules per square centimeter to 100 joules per square centimeter.
 10. The method according to claim 1 wherein the laser beam pulse defines a spot in or on the material and the LIB causes ablation of an area having a size smaller than the area of the spot.
 11. The method according to claim 1 wherein the laser beam pulse has a wavelength in a range of 200 nanometers to 2 microns.
 12. The method according to claim 1 wherein the pulse width is in a range of a few picoseconds to femtoseconds.
 13. The method according to claim 1 wherein the breakdown includes changes caused by one or more of ionization, free electron multiplication, dielectric breakdown, plasma formation, and vaporization.
 14. The method according to claim 1 wherein the breakdown includes plasma formation.
 15. The method according to claim 1 wherein the breakdown includes disintegration.
 16. The method according to claim 1 wherein the breakdown includes ablation.
 17. The method according to claim 1 wherein the breakdown includes vaporization.
 18. The method according to claim 1 wherein the spot size is varied by flexible diaphragm to a range of 1 to 100 microns.
 19. The method according to claim 1 wherein a mask is placed in the path of the beam to block a portion of the beam to cause the beam to assume a desired geometric configuration.
 20. The method according to claim 1 wherein the laser operating mode is non-TEMoo.
 21. The method according to claim 1 wherein the laser beam pulse defines a spot and has a lateral gaussian profile characterized in that fluence at or near the center of the beam pulse spot it is greater than the threshold fluence whereby the laser induced breakdown is ablation of an area within the spot.
 22. The method according to claim 22 21wherein the spot size is a diffraction limited spot size providing an ablation cavity having a diameter less than the fundamental wavelength size.
 23. The method according to claim 1 wherein the characteristic pulse width is obtained by determining the ablation (LIB) threshold of the material as a function of pulse width and determining where the ablation (LIB) threshold function is no longer proportional to the square root of pulse width.
 24. A method for laser induced breakdown of a material which comprises: a. generating a beam of one or more laser pulses in which each pulse has a pulse width equal to or less than a pulse width value corresponding to a change in slope of a curve of fluence breakdown threshold (F_(th)) as a function of laser pulse width (T), said change occurring at a point between first and second portions of said curve, said first portion spanning a range of relatively long pulse width where F_(th) varies with the square root of pulse width (T^(1/2)) and said second portion spanning a range of short pulse width relative to said first portion with a F_(th) versus T slope which differs from that of said first portion; and b. focusing directing said one or more pulses of said beam to a point at or beneath the surface of the material.
 25. The method according to claim 24 and further including: a. identifying a pulse width start point; b. focusing directing the laser beam initial start point at or beneath the surface of the material; and c. scanning said beam along a predetermined path in a transverse direction.
 26. The method according to claim 24 and further including: a. identifying a pulse width start point; b. focusing directing the laser beam initial start point at or beneath the surface of the material; and c. scanning said beam along a predetermined path in a longitudinal direction in the material to a depth smaller than the Rayleigh range.
 27. The method according to claim 24 wherein the breakdown includes changes caused by one or more of ionization, free electron multiplication, dielectric breakdown, plasma formation, and vaporization.
 28. The method according to claim 24 wherein the breakdown includes plasma formation.
 29. The method according to claim 24 wherein the breakdown includes disintegration.
 30. The method according to claim 24 wherein the breakdown includes ablation.
 31. The method according to claim 24 wherein the breakdown includes vaporization.
 32. The method according to any one of claims 1, 2, 5 or 24 wherein said beam is obtained by chirped-pulse amplification (CPA) means comprising means for generating a short optical pulse having a predetermined duration; means for stretching such optical pulse in time; means for amplifying such time-stretched optical pulse including solid state amplifying media; and means for recompressing such amplified pulse to its original duration.
 33. A method for laser induced breakdown (LIB) of a non-organic material with a pulsed laser beam, the material being characterized by a relationship of fluence breakdown threshold at which breakdown occurs versus laser pulse width that exhibits a rapid and distinct change in slope at a predetermined laser pulse width where the onset of plasma induced breakdown occurs, said method comprising the steps of: a. generating a beam of at least one or more laser pulses in which each pulse has a pulse width equal to or less than said predetermined laser pulse width; and b. focusing said beam directing said pulse to a point at or beneath the surface of the material so that the laser beam defines a spot and has a lateral gaussian profile characterized in that fluence at or near the center of the beam spot is greater than the threshold fluence whereby the laser induced breakdown is ablation of an area within the spot.
 34. The method according to claim 33 wherein the spot size is a diffraction limited spot size providing an ablation cavity having a diameter less than the fundamental wavelength size.
 35. A method for laser induced breakdown (LIB) of a non-biologic material with a pulsed laser beam, the material being characterized by a relationship of fluence breakdown threshold at which breakdown occurs versus laser pulse width that exhibits a rapid and distinct change in slope at a predetermined laser pulse width where the onset of plasma induced breakdown occurs, said method comprising the steps of: a. generating a beam of at least one or more laser pulses in which each pulse has a pulse width equal to or less than said predetermined laser pulse width; and b. focusing said beam directing said pulse to a point at or beneath the surface of the material which is biological tissue , the pulse width is 10 to 10,000 femtoseconds and the beam has an energy of 10 nanojoules to 1 millijoule.
 36. A method for laser induced breakdown (LIB) of a material by plasma formation with a pulsed laser beam, the material being characterized by a relationship of fluence breakdown threshold at which breakdown occurs versus laser pulse width that exhibits a distinct change in slope at a characteristic laser pulse width, said method comprising the steps of: a. generating a beam of at least one or more laser pulses in which each pulse has a pulse width equal to or less than said characteristic laser pulse width, said characteristic pulse width being defined by the ablation (LIB) threshold of the material as a function of pulse width where the ablation (LIB) threshold function is no longer proportional to the square root of pulse width; and b. focusing said beam directing said pulse to a point at or beneath the surface of the material and inducing breakdown by plasma formation in the material.
 37. A method for laser induced breakdown of a material which comprises: a. determining, for a selected material, characteristic curve of fluence breakdown threshold (F_(th)) as a function of the square root of laser pulse width; b. identifying a pulse width value on said curve corresponding to a rapid and distinct change in slope of said F_(th) versus pulse width curve the relationship between the fluence breakdown and the square root of pulse width characteristic of said material; c. generating a beam of one or more laser pulses, said pulses having a pulse width at or below said pulse width value corresponding to said distinct change in slope; and d. focusing directing said one or more pulses of said beam to a point at or beneath the surface of the material.
 38. The method according to claim 37 and further including: a. identifying a pulse width start point; b. focusing directing the laser beam initial start point at or beneath the surface of the material; and c. scanning said beam along a predetermined path in a transverse direction.
 39. The method according to claim 37 and further including: a. identifying a pulse width start point; b. focusing directing the laser beam initial start point at or beneath the surface of the material; and c. scanning said beam along a predetermined path in a longitudinal direction in the material to a depth smaller than the Rayleigh range.
 40. The method according to claim 37 wherein the breakdown includes changes caused by one or more of ionization, free electron multiplication, dielectric breakdown, plasma formation, and vaporization.
 41. The method according to claim 37 wherein the breakdown includes plasma formation.
 42. The method according to claim 37 wherein the breakdown includes disintegration.
 43. The method according to claim 37 wherein the breakdown includes ablation.
 44. The method according to claim 37 wherein breakdown includes vaporization.
 45. The method according to any one of claims 35, or 37 wherein said beam is obtained by chirped-pulse amplification (CPA) means comprising means for generating a short optical pulse having a predetermined duration; means for stretching such optical pulse in time; means for amplifying such time-stretched optical pulse including solid state amplifying media; and means for recompressing such amplified pulse to its original duration.
 46. A method for laser induced breakdown (LIB) of a metallic material with a pulsed laser beam, the material being characterized by a relationship of fluence threshold at which breakdown occurs versus laser pulse width that exhibits a distinct change in slope at a characteristic laser pulse width, said method comprising the steps of: generating at least one laser pulse which has a pulse width equal to or less than said characteristic laser pulse width, said pulse having a width between 10 and 10,000 femtoseconds, and the pulse has an energy of 1 nanojoule to 1 microjoule; and directing the pulse to a point at or beneath the surface of the material.
 47. A method as in claim 46 wherein said beam is obtained by chirped pulse amplification (CPA) means comprising means for generating a short optical pulse having a predetermined duration; means for stretching such optical pulse in time; means for amplifying such stretched optical pulse including solid state amplifying media; and means for recompressing such amplified pulse to its original duration.
 48. A method for laser induced breakdown (LIB) of a metallic material transparent to radiation with a pulsed laser beam, the material being characterized by a relationship of fluence threshold at which breakdown occurs versus laser pulse width that exhibits a distinct change in slope at a characteristic laser pulse width, said method comprising the steps of: generating at least one laser pulse which has a pulse width equal to or less than said characteristic laser pulse width, where the laser pulse width is 10 to 10,000 femtoseconds and the laser pulse has an energy of 10 nanojoules to 1 millijoule; and directing the pulse to a point at or beneath the surface of the material.
 49. A method as in claim 48 wherein said beam is obtained by chirped pulse amplification (CPA) means comprising means for generating a short optical pulse having a predetermined duration; means for stretching such optical pulse in time; means for amplifying such stretched optical pulse including solid state amplifying media; and means for recompressing such amplified pulse to its original duration.
 50. A method for laser induced breakdown (LIB) of a metallic material with a pulsed laser beam, the material being characterized by a relationship of fluence threshold at which breakdown occurs versus the square root of laser pulse width that exhibits a distinct change in slope at a characteristic laser pulse width; determining the ablation (LIB) threshold of the material as a function of pulse width and determining where the ablation (LIB) threshold function is no longer proportional to the square root of pulse width; generating at least one laser pulse which has a pulse width equal to or less than the characteristic pulse width; and directing the pulse to a point at or beneath the surface of the material.
 51. A method of optimally selecting a pulse width and fluence for a pulsed laser beam such that the pulsed laser induces laser induced breakdown (LIB) of a material, the material being characterized by a relationship of fluence threshold at which breakdown occurs versus the square root of laser pulse width comprising the step of identifying where the relationship between fluence threshold and the square root of pulse width exhibits a distinct change in slope and selecting the pulse width and fluence level associated with the distinct change in slope and directing the pulse at a point at or beneath the surface of the material.
 52. The method as in claim 51 wherein the material is non-organic.
 53. A method as in claim 51 wherein the material is organic.
 54. A method for laser induced breakdown of a material with a pulsed laser beam, the material being characterized by a relationship of fluence threshold at which breakdown occurs versus the square root of laser pulse width that exhibits a distinct change in slope at a characteristic pulse width, said method comprising the steps of: selecting a pulse width and fluence which is equal to or less than the distinct change in slope; generating at least one laser pulse which has a pulse width equal to or less than the characteristic laser pulse width and fluence; and directing said pulse to a point at or beneath the surface of a material. 